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Finding the Third Proportional to 513 and 589.50

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Solution

The third proportional to 513 and 589.50 is: 677.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    513 : 589.50 = 589.50 : x
  2. Step 2: Convert to fraction form
    513/589.50 = 589.50/x
  3. Step 3: Cross multiply
    513x = 589.50 × 589.50
  4. Step 4: Simplify right side
    513x = 347,510.25
  5. Step 5: Solve for x
    x = 347,510.25/513
  6. Step 6: Final answer
    x = 677.41

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Why These Related Problems?

These problems maintain the same ratio (1.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.